Solve for x: 2x - 1 = -35
Show algebraic work: __________________________________
CCSS 7.EE.B.4a · px + q = r and p(x + q) = r
Two-Step Equations Worksheet Generator
Generate equations directly from the two forms named in 7.EE.B.4a. Solutions are constructed first and the equation is built around them, so rational coefficients remain exact and every answer can be verified by substitution.
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Solve Two-Step Equations
Solve two-step equations · Grade 7 standard · Seed 271801
1.
2.
Solve for x: 4x - 4 = 24
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3.
Solve for x: 1/2x - 5/2 = -21/4
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4.
Solve for x: 2(x - 12) = -6
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5.
Solve for x: 6x - 7/2 = -43/2
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6.
Solve for x: -1/2x - 3 = -17/2
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7.
Solve for x: -4x + 1 = 17
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8.
Solve for x: -4x + 8 = -38
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9.
Solve for x: 2x + 2 = 46
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10.
Solve for x: -6x + 7 = -62
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Construction rule: equations are built around known exact solutions, expression rewrites use exact rational arithmetic, 7.EE.3 money stays in integer cents, and inequality answer graphs are withheld until answers are revealed.
Solving a two-step equation
To solve a two-step equation, undo the operations in reverse order: first undo the addition or subtraction, then undo the multiplication or division. Do the same thing to both sides to keep the equation balanced. Check the answer by substituting it into the original equation.
Worked examples
- 2x + 3 = 11: subtract 3 from both sides to get 2x = 8, then divide by 2 to get x = 4. Check: 2(4) + 3 = 11.
- x/3 − 2 = 5: add 2 to get x/3 = 7, then multiply both sides by 3 to get x = 21.
- −4x + 5 = −7: subtract 5 to get −4x = −12, then divide by −4 to get x = 3.
Common slips
- Dividing only one term first. In 2x + 3 = 11, dividing by 2 gives x + 1.5 = 5.5, so every term must be divided.
- Sign errors with negatives. −12 ÷ (−4) is positive 3, not −3.
- Doing an operation to one side only, which unbalances the equation.
How to use this worksheet
Ask students to write each step under the equation and to check by substituting the answer. The answer key shows the value of x, so students can tell whether an error came from the solving or the check.
Common Core connection
- 7.EE.B.4 · Use variables and equations or inequalities to solve problems and explain solutions.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Classroom note 1
For px + q = r, undo q before dividing by p; this is reverse order of operations.
Classroom note 2
For p(x + q) = r, either divide by p first, then undo q inside the parentheses, or distribute p first and solve as px + pq = r.
Classroom note 3
Keep the equation balanced: apply the same operation to both sides on the same line.
Classroom note 4
Watch the sign of q: solving 3x - 8 = 7 adds 8 to both sides, so 3x = 15 and x = 5.
Classroom note 5
Check the solution by substitution into the original equation, not only into an intermediate line.
Continue the 7.EE progression
Move to another Grade 7 algebra skill
Questions people ask
Do equations include fractions?
Yes. Standard and challenge modes can include rational coefficients and rational solutions.
Are variables on both sides included?
No. This route stays with the equation forms named in Grade 7 standard 7.EE.B.4a rather than drifting into later algebra.
How is p(x + q) = r different from px + q = r?
In p(x + q) = r the whole quantity x + q is multiplied by p, so p must be cleared from every term inside. In px + q = r only x is multiplied by p, and q is added afterward.
Why require a substitution check?
Substituting the solution back into the original equation catches sign slips and inverse-operation mistakes that a later line in the work would carry forward unnoticed.